Home
Class 12
MATHS
If x^m occurs in the expansion (x+1//x^2...

If `x^m` occurs in the expansion `(x+1//x^2)^(2n)` , then the coefficient of `x^m` is a.`((2n)!)/((m)!(2n-m)!)` b. `((2n)!3!3!)/((2n-m)!)` c. `((2n)!)/(((2n-m)/3)!((4n+m)/3)!)` d. none of these

A

`((2n)!)/((m!)(2n-m)!)`

B

`((2n)!3!3!)/((2n-m)!)`

C

`((2n)!)/(((2n-m)/(3))!((4n+m)/(3))!)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise LEVEL 2|50 Videos
  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise NUMERICAL VALUE TYPE FOR JEE MAIN|14 Videos
  • BINOMIAL THEOREM

    VMC MODULES ENGLISH|Exercise JEE Archive|56 Videos
  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

Similar Questions

Explore conceptually related problems

If x^p occurs in the expansion of (x^2+1//x)^(2n) , prove that its coefficient is ((2n)!)/([1/3(4n-p)]![1/3(2n+p)]!) .

If x^p occurs in the expansion of (x^2+1//x)^(2n) , prove that its coefficient is ((2n)!)/([1/3(4n-p)]![1/3(2n+p)]!) .

If x^p occurs in the expansion of (x^2 + (1)/(x) )^(2n) , prove that its coefficient is ((2n)!)/( [ (1)/(3) (4n - p)!][(1)/(3) (2n + p) !])

Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-l)))^(1//(l-m))*(x^((n+l)/(l-m)))^(1//(m-n)) wrt x is

If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

If 'n' is a positive integer then prove that the coefficient fo x^(m) in the expansion of (x^(2)+(1)/(x))^(2n) is :

If in the expansion of (1 +x)^(m) (1 - x)^(n) , the coefficients of x and x^(2) are 3 and - 6 respectively, the value of m and n are

The middle term in the expansion of ((2x)/3-3/(2x^2))^(2n) is a. \ ^(2n)C_n b. (-1)^n\ ^(2n)C_(n\ )x^(-n) c. \ ^(2n)C_n x^(-n) d. none of these

In the expansion of (x^2+2x+2)^n, n in N (A) coefficient of x=n.2^n (B) coefficient of x^2=n^2 2^(n-1) (C) coefficient of x^3=n^2 2^(n-2) (D) none of these

The coefficient of x^r[0lt=rlt=(n-1)] in the expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^2+.... +(x+2)^(n-1) is a.^n C_r(3^r-2^n) b.^n C_r(3^(n-r)-2^(n-r)) c.^n C_r(3^r+2^(n-r)) d. none of these

VMC MODULES ENGLISH-BINOMIAL THEOREM-LEVEL 1
  1. Find the number of nonzero terms in the expansion of (1+3sqrt(2)x)^9+(...

    Text Solution

    |

  2. Find the coefficient of x^(20) in (x^2+2+1/(x^2))^(-5)(1+x^2)^(40)dot

    Text Solution

    |

  3. If x^m occurs in the expansion (x+1//x^2)^(2n) , then the coefficient ...

    Text Solution

    |

  4. Find the coefficient of x^5 in the expansion of (1+x)^(21)+(1+x)^(22)+...

    Text Solution

    |

  5. If n > 1 is an integer and x!=0, then (1 +x)^n-nx-1 is divisible by

    Text Solution

    |

  6. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c...

    Text Solution

    |

  7. The numberof integral termsin the expansion of ( (3)-root(8)(5))^256 i...

    Text Solution

    |

  8. Find the coefficient of x^(13) in the expansion of (1-x)^5xx(1+x+x^2+x...

    Text Solution

    |

  9. If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, the...

    Text Solution

    |

  10. Find the positive integer just greater than (1+0. 0001)^(10000)dot

    Text Solution

    |

  11. The term independent of a in the expansion of (1+sqrt(a)+1/(sqrt(a)-1)...

    Text Solution

    |

  12. The coefficient of x^(53) in the expansion sum(m=0)^(100)^(100)Cm(x-3)...

    Text Solution

    |

  13. In the binomial expansion of (a - b)^n , n ge 5 the sum of the 5th ...

    Text Solution

    |

  14. The range of values of the term independent of x in the expansion ...

    Text Solution

    |

  15. Find the sum +^(10)C1+^(10)C3+^(10)C5+^(10)C7+^(10)C9dot

    Text Solution

    |

  16. Let n in N. If (1+x)^(n)=a(0)+a(1)x+a(2)x^(2)+…….+a(n)x^(n) and a(n)-3...

    Text Solution

    |

  17. The greatest coefficient in the expansion of (1+x)^(2n) is

    Text Solution

    |

  18. If (1-x+x^2)^n=a0+a1x+a2x^2+ .........+a(2n)x^(2n),\ find the value o...

    Text Solution

    |

  19. The value of sum(i=0)^(n)""^(n-i)C(r),rin[1,n]capsquare is equal to :

    Text Solution

    |

  20. The value of (""^(47)C(4))/(""^(57)C(4))+sum(j=0)^(3)(""^(50-j)C(3))/(...

    Text Solution

    |